Male Pagurus minutus hermit crabs use multiple types of information in decisions to give up male–male contests

Organisms use information to make adaptive decisions in various contexts, including aggression. Potentially weaker, but better-informed, contestants should give up earlier to reduce fighting costs by using information related to their own lower success such as their size relative to their opponent and past contest outcomes to make this choice. Here, we examined whether intruders of the hermit crab Pagurus minutus could use information about their (1) smaller size, (2) past contest defeats, (3) opponent’s past wins, or (4) relationship in the dominance hierarchy to their opponent when making a decision to give up during male–male contests for a female. In all trials, we randomly matched a smaller intruder with a larger opponent that was guarding a female. Our analyses suggest that P. minutus intruders can use all four types of information to decide whether to give up a contest without escalation or decrease its duration after escalation; it is the first species of Pagurus reported to do so, and the second reported to be able to distinguish familiar opponents from others in the context of male–male contests. These findings demonstrate the importance of cognitive abilities in minimizing costs when competing for vital resources.

information about their chance of success, such as their relative size, their own recent defeats or their opponent's recent wins, and the dominance hierarchy with their opponent.
Yasuda et al. 28 examined whether these four factors affect the decision of P. middendorffii intruders to give up by using pairs of randomly selected smaller intruders and larger guarding males (i.e., random-sized method 19 ).This species shows a large size advantage in male-male contests 26 , and smaller intruders are less likely to escalate fights 23 .This avoidance increased when smaller intruders encountered unfamiliar larger opponents with previous experience of wins, and avoidance was greatest when they re-encountered familiar opponents that had established dominance hierarchy 28 .Their own experience of defeat, however, did not affect the decision to give up in this species 28 .Thus, smaller intruders of P. middendorffii appear to use three types of information for their decision, but not their own defeats.
Pagurus minutus is another species in which the effects of information on the intruder's decision to give up has been investigated.Pagurus minutus also shows a large size advantage and a lower probability of escalation by smaller intruders 29,30 .Yasuda et al. 31 reported that P. minutus intruders with previous defeats had decreased eventual fighting success against unfamiliar naïve guarders.Although this suggests that individuals of this species collect information about experience of defeat, the effect of this information on the decision to give up is still unclear, because the study did not assess whether and when the losers gave up.More importantly, it used pairs of similar-sized males (i.e., self-selection method 19 ) to clarify the effect of factors other than male size (i.e., female size in that study) on male-male contests.Hsu et al. 19 recommend the random-sized method to examine the effect of experience, because the relationship between size and RHP is not perfect, even between similarsized contestants.No study has tested whether P. minutus can use information related to opponent status and established hierarchy.
Here, we examined whether the decision of P. minutus intruders to give up is affected by four types of potentially available information related to RHP, namely (1) size relative to their opponent, (2) previous defeats, (3) opponent's previous wins, and (4) established dominance hierarchy with the same opponent.We used randomlyselected males in male-male contests according to the suggestion of Hsu et al. 19 (also see Yasuda et al. 31 ).

Study animals
We collected precopulatory guarding pairs of P. minutus, each male with an intact major cheliped, from a sandy mud flat at Nunohiki, in the Waka River estuary, Wakayama, Japan (34°10′23″N, 135°10′49″E), from December 2015 to February 2016; the mating season of this species at this site occurs from November to April 32 .Each pair was placed in a small vinyl pouch filled with seawater collected in the field.In the laboratory, pairs in which the male was still guarding the female were separated, and each individual was kept in a container (8 cm × 12.5 cm × 8 cm) or a plastic cup (200 mL) with natural seawater (2.5 cm deep), to prevent copulation before the experiment.All pairs were acclimatized to laboratory conditions for at least 1 h before the experiment, and all tests were conducted within 6 h of collection.
After the experiments, all crabs were fixed by freezing (− 18°C) to allow us to measure them.The shield length (SL, calcified anterior portion of the cephalothorax, index of body size) of all males was then measured to the nearest 0.01 mm under a stereomicroscope.Since female size has no effect on random-sized male-male contests in this species 29,30 , we excluded this value.

Experimental design
We performed two sequential trials of male-male contests (Trials 1 and 2).In Trial 1, two guarding pairs were randomly assigned to an experimental set (N = 92 sets), and in each set the smaller male was designated as the intruder and the larger male as the guarder, owing to the large size advantage in this species 29 .We then placed a guarding male and his guarded female in a small plastic arena (19.5 cm × 11.0 cm × 8.5 cm) containing seawater about 3 cm deep.After the guarder had returned to guarding the female, the intruder was placed in the arena.We checked the outcome of Trial 1 at 15 min from when the intruder initiated movement; all intruders lost Trial 1 (i.e., did not guard a contested female).
Each intruder was then used again as an intruder in a second trial (Trial 2) after 1 h had elapsed.In Trial 2, we assigned the losers to three experimental groups with different types of guarders.In Group 1, losers encountered larger guarders that had not participated in Trial 1 (N = 31 sets).In Group 2, losers encountered guarders that won Trial 1 against a different intruder (N = 30 sets).In Group 3, losers encountered the same guarders as in Trial 1 (N = 31 sets).The difference in SL between losers and guarders did not differ significantly among groups (ANOVA, F 2,89 = 1.030,P = 0.361).Other experimental methods in Trial 2 were the same as in Trial 1.
We recorded all trials using a digital camera (DMC-LF1, Panasonic) from the time the individuals were introduced into the arena until 15 min after the intruder began moving.When the intruder initiated grappling with the guarder (for details of this behavior, see 23 ), we considered that the trial had escalated.After escalation, if intruders did not perform physical aggression for more than 3 min, we defined the fight as settled.We then recorded the duration (seconds) of the series of aggressive interactions as the contest duration until the intruder gave up and the eventual outcome on the basis of which male was guarding the female.Because the duration was defined as ending when the intruder gave up, we excluded contests in which the intruder won (Group 1, N = 1 set; Group 2, N = 1 set; Table 1) from the following analyses.If males continued grappling, with both males grabbing the shell of the contested female, at the end of Trial 2, the trial was defined as a draw (Group 1, N = 1 set; Table 1), and the duration until giving up the trial was censored.The final sample sizes for the analyses were 30 in Group 1, 29 in Group 2, and 31 in Group 3 (Table 1).No crabs were injured or lost any appendages during either trial.
Since the contest duration of Trial 1 had no effect on the decision to give up without escalation in Trial 2 in Group 1 (see Supplementary Fig. S1), we considered that the loser's behavior in Trial 2 was independent of energy depletion from Trial 1.

Analyses
Data from Trial 1 were used to examine whether the intruder's decision to give up was affected by the opponent's relative size.For giving-up without escalation, a generalized linear model (GLM) with a binomial error distribution was used.This model was constructed by using whether intruders gave up without escalation (Yes = 1, No = 0; N = 90) as the response variable and the SL difference between intruders and guarders (DSL I-G ) as the explanatory variable.Contest duration until giving-up was analyzed by Cox's proportional hazard model 33 .The response variable in this model was contest duration (sec, N = 70), and the explanatory variable was DSL I-G .
We then used data from both trials in Group 1 to examine the effect of a defeat in Trial 1 on the decision in Trial 2. Since we observed all intruders twice, we used a generalized linear mixed model (GLMM) and Cox's model with mixed effects to control for pseudo-replication.In the GLMM, the response variable was whether intruders gave up without escalation (Yes = 1, No = 0; N = 30 × 2 = 60), and the explanatory variables were (1) Trial (Trial 1 or 2) and ( 2) DSL I-G .In the mixed Cox's model, the response variable was contest duration (sec; N = 23 + 14 = 37), and the explanatory variable was the same as in the GLMM (i.e., (1) and ( 2)).Intruder ID was treated as a random factor in both analyses.
The GLMM for giving-up frequency and the mixed Cox's model for contest duration were also used to assess whether the intruder's decision was affected by the opponent's previous wins (Group 1 vs. Group 2; losers faced naïve opponents or opponents that won the previous contest) and established hierarchy with the same opponent (Group 2 vs. Group 3; losers faced a different or the same opponent that won the previous contest).In the GLMMs (Group 1 vs. 2, N = [30 × 2] + [29 × 2] = 118; Group 2 vs. 3, N = [29 × 2] + [31 × 2] = 120), the explanatory variables were (1) Trial (Trial 1 or 2), (2) Group (Group 1 vs. Group 2 or Group 2 vs. Group 3), and (3) DSL I-G .In the mixed Cox's model (Group 1 vs. Group 2, N = 23 + 14 + 22 + 15 = 74; Group 2 vs. Group 3, N = 22 + 15 + 25 + 7 = 69), all three explanatory variables were included.To examine the effect of information, we also added a (4) Trial × Group interaction in each model if the interaction was significant.Intruder ID was treated as a random effect in all four models.
All analyses in this study were performed in R v. 4.1.1 34software, and the R packages "glmmML" 35 and "coxme" 36 were used to conduct the GLMM and Cox's model with mixed effects analyses.In Cox's model, the proportional hazard assumption was satisfied for all explanatory variables (P > 0.062), except for a Trial × Group interaction in the model comparing Groups 2 and 3 (P = 0.034).However, since this model was not used in this study because the Trial × Group interaction was not significant (see "Results"), we concluded the proportional hazard assumption to be acceptable.

Relative size
In Trial 1, the frequency of giving-up without escalation significantly increased as DSL I-G decreased (z = − 3.234, P = 0.001; Fig. 1a).After escalation, smaller intruders also showed significantly earlier giving-up (z = − 3.435, P < 0.001; Fig. 1b).Details of these and following analyses are shown in Supplementary Table S1.

Opponent's prior wins
In the comparison between Groups 1 and 2, Trial × Group interaction was excluded from the GLMM because it was not significant (z = − 0.562, P = 0.574).In the GLMM without the interaction, giving-up without escalation was significantly affected by Trial and DSL I-G but not by Group (Trial: z = 2.925, P = 0.003; DSL I-G : z = − 2.512, Table 1.Experimental groups for two sequential trials of male-male contests in Pagurus minutus.*1 Data from Trial 1 were divided for analyses focusing on each group (see text).*2 These data were excluded from the analysis since our aim was to examine intruders' giving-up decisions; N = 90 for Trial 1 in analyses.www.nature.com/scientificreports/P = 0.012; Group: z = − 0.412, P = 0.680).The frequency of intruders that did not escalate was higher in Trial 2 than in Trial 1 of both groups (Fig. 3a) and increased as DSL I-G decreased.
In the mixed Cox's model, Trial × Group interaction was significant (z = 2.362, P = 0.018).While contest duration until giving-up was similar between trials in Group 1, it was lower in Trial 2 than in Trial 1 in Group 2 (Fig. 3b).However, although Trial 1 was the same for all groups, duration in Trial 1 seemed shorter in Group 1 than in Group 2 (Fig. 3b; see also Fig. 4b for the value of Group 3).The significant Trial × Group interaction might have been caused by this unexpected difference.Smaller intruders gave up significantly sooner after escalation (z = − 2.592, P = 0.010).

Established dominance hierarchy
In the comparison between Groups 2 and 3, the Trial × Group interaction was significant in the GLMM (z = 2.182, P = 0.029).Although the frequency of giving-up without escalation increased in Trial 2 in both groups, the intensity of the trend was greater in Group 3 than in Group 2 (Fig. 4a).DSL I-G also had a significant effect on the decision (z = − 2.897, P = 0.004).
In the mixed Cox's model, we excluded the Trial × Group interaction from the model because it was not significant (z = − 0.374, P = 0.710).In the mixed Cox's model without the interaction, intruders gave up significantly  No difference was found between groups (z = 0.037, P = 0.970).

Discussion
We conducted random-sized male-male contests of the hermit crab P. minutus to examine whether smaller solitary intruders give up contests earlier on the basis of four types of information: size relative to a larger guarding opponent, previous defeats, opponent's previous wins, and the established dominance hierarchy.We found that three factors increased the frequency of giving-up without escalation: smaller size (Trial 1; Fig. 1a), a previous defeat (Trial 1 vs. Trial 2 in Group 1; Fig. 2a), and re-encountering the same dominant opponent (Group 2 vs. Group 3 in Trial 2; Fig. 4a).The opponent's previous wins, on the other hand, appeared to contribute to a shorter duration after escalation (Group 1 vs. Group 2 in Trial 2; Fig. 3b).Our previous studies have also shown that the motivation of P. minutus intruders to fight is decreased when they encounter a larger opponent in the randomly-chosen contests 29,30 and had experienced a recent defeat in the similar-sized contests 31 .This is the first study to show that Pagurus hermit crab intruders can use all four types of information to decide whether to give up male-male contests and to confirm that the intruders use information about their recent defeats regardless of the experimental method.

Figure 1 .
Figure 1.Relationship between male size difference and (a) intruders' frequency of giving-up without escalation and (b) contest duration after escalation.DSL I-G indicates difference in shield length (index of body size) between intruders and guarders.Number in parentheses in (b) indicates sample size.

Figure 2 .
Figure 2. Relationship between trials and (a) the frequency of giving-up without escalation by intruders and (b) duration until giving-up by intruders after escalation.Number in parentheses in (a) indicates sample size in Group 1.

Figure 3 .
Figure 3. Differences between Groups 1 and 2 in (a) the frequency of giving-up without escalation by intruders and (b) duration until giving-up by intruders after escalation.Numbers in parentheses in (a) indicate sample size.Group 1: naïve opponent; Group 2: opponent that won against a different intruder.

Figure 4 .
Figure 4. Differences between Groups 2 and 3 in (a) the frequency of giving-up without escalation by intruders and (b) duration until giving-up by intruders after escalation.Numbers in parentheses in (a) indicate sample size.Group 2: opponent that won against a different intruder; Group 3: same opponent as in Trial 1.